# Video Tutorial – The Hazard Function is the Probability Density Function Divided by the Survival Function

In an earlier video, I introduced the definition of the hazard function and broke it down into its mathematical components.  Recall that the definition of the hazard function for events defined on a continuous time scale is $h(t) = \lim_{\Delta t \rightarrow 0} [P(t < X \leq t + \Delta t \ | \ X > t) \ \div \ \Delta t]$.

Did you know that the hazard function can be expressed as the probability density function (PDF) divided by the survival function? $h(t) = f(t) \div S(t)$

In my new Youtube video, I prove how this relationship can be obtained from the definition of the hazard function!  I am very excited to post this second video in my new Youtube channel.

### 2 Responses to Video Tutorial – The Hazard Function is the Probability Density Function Divided by the Survival Function

1. skaae says:

Thanks for the explanation. The first time someone explained what appears to be a fact in most text books! I suggest you break down the partial likelihood in Cox models as well 🙂

• Eric Cai - The Chemical Statistician says:

I’m glad that it was useful to you! I will discuss Cox models and partial likelihoods eventually – thanks for the suggestion!